Geneticists wanted to know if a particular gene is associat

. Geneticists wanted to know if a particular gene is associated with differential survival of male and female larvae. So, they obtained a generation of fruit flies with the same genotype, and counted numbers of male and female adults, after the larval stage. If the gene does not affect larval survival differently, then the sex ratio will be even for adults (i.e. 50% male).

Here are the data:

            Males              35

            Females           46

Choose an approach for analyzing these data that meets the research goals.

Solution

We design a proportion z test, that is, if p = the proportion of males, then

Ho: p = 0.5
Ha: p =/= 0.5

Then, we may set a 0.05 significance level.

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Formulating the null and alternatuve hypotheses,          
          
Ho:   p   =   0.5
Ha:   p   =/=   0.5

As we see, the hypothesized po =   0.5      

Getting the point estimate of p, p^,          
          
p^ = x / n =    0.432098765      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.055555556      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -1.222222222      
          
As this is a    2   tailed test, then, getting the p value,  
          
p =    0.221623602      
significance level =    0.05      

As P > 0.05, we   FAIL TO REJECT THE NULL HYPOTHESIS.  

Thus, there is no significant evidence that the gene affects larval survival differently. [CON LUSION]